Representation of Geophysical Maps with Uncertainty

This paper proposes a method for the reconstruction of surfaces from spatially distributed geophysical data with uncertainties. For efficient interrogation and storage and the ability to represent uncertainty, bi-quadratic uniform integral enveloping or interval B-spline surfaces are fit to uniformly distributed cellular data using linear programming methods. The cellular data function is characterized by an upper and lower bound of the measured values for a range (box) of the independent variables. Interior patch boundaries are formed using a quadtree segmentation of the data set and interior knots are placed according to an algorithm for edge detection. C 1 continuity across patch boundaries is maintained by initially fitting auxiliary patches which then define the boundary conditions for the interior patches. A map from measured geophysical data illustrates the method.

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